Local Models in F-Theory and M-Theory with Three Generations

TL;DR

This paper develops a geometric framework for constructing local phenomenological models with three generations in F-theory and M-theory, highlighting the role of ALE-fibrations and their generic structures.

Contribution

It introduces a unified geometric approach to engineer realistic three-generation models in F-theory and M-theory using ALE-fibrations, connecting their structures.

Findings

Geometric structures for interactions are generic in ALE-fibrations.

Models with three generations are achievable within E8-ALE constraints.

The framework links F-theory and M-theory constructions through geometric correspondence.

Abstract

We describe a general framework that can be used to geometrically engineer local, phenomenological models in F-theory and M-theory based on ALE-fibrations, and we present several concrete examples of such models that feature three generations of matter with semi-realistic phenomenology. We show that the geometric structures required for generating interactions--triple-intersections of matter-curves in F-theory and supersymmetric three-cycles supporting multiple conical singularities in M-theory--are generic in such ALE-fibred manifolds, and that they can be understood in correspondence with one another. The models we can construct in this way are strictly limited in complexity by the maximality of the E8-ALE space, but turn out to be just complex enough to accommodate some of the most realistic string models to date.